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]]>**Unofficial schedule**

__Classic Math Circle Problems__

Dates: Thursdays, 3:30-4:30pm, 9/20-10/18 (5 weeks)

Suggested Ages: 5-7

Knights and Liars, open questions, story problems, pattern making and breaking, explorations of infinity, proofs, and more. We will have fun with these classic math circle activities as students develop the mathematical-thinking skills of asking questions, forming conjectures, testing conjectures, and generally seeking the underlying structure of things.

__ __

__Category Theory__

Dates: Thursdays, 3:30-4:45pm, 10/25-12/6 (6 weeks, 75-minute sessions, 7.5 hours total, no class on Thanksgiving)

Suggested Ages: 10-14

Mathematician Eugenia Cheng describes category theory as “the mathematics of mathematics.” Inspired by Cheng’s book “How to Bake Pi,” we will do activities that use abstract mathematics to see, understand, and generalize the defining structure of things. And by “things” I mean mathematical things, logical things, and social phenomena. Visit her website (eugeniacheng.com) for a preview.

__Queen Dido Problems__

Dates: Thursdays, 3:30-4:45pm, 1/24-3/21 (8 weeks, 75-minute sessions, 10 hours total, no class on 3/7)

Suggested Ages: 13+

In this course, students will explore real mathematics problems from ancient history. These will include Queen Dido problems, Zeno’s Paradox, and ancient inheritance problems. We’ll do the math and put the problems in their historical contexts. We may dabble in a few mythological problems as well. Mathematical concepts will include pre-algebra, algebra, geometry, and some calculus, but pre-requisite knowledge of these topics is not required.

__Polyominoes and Functions__

Dates: Thursdays, 3:30-4:30pm, 4/4-5/16 (6 weeks)

Suggested Ages: 8-10

Polyominoes are a hands-on geometry activity that develop students’ thinking about classification, combinatorics, symmetry, and more. We will also study characteristics of functions via the book Funville Adventures (or via extensions of this book if the students have already used it) and function machines in order to develop algebraic reasoning skills.

(registration information should be posted within a week)

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]]>The post Open House: Thursday, May 31, 2018 appeared first on Talking Stick Learning Center.

]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 4-17. We will be hosting the entire open house at our Garden Classroom. We have several families attending with young people in different age groups, so we are planning to have all ages, all programs meet in one location.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Thursday, May 31st, 2018

**TIME:** 10:00 a.m. to 12:00 p.m.

**LOCATION:** The Garden Classroom at Awbury Arboretum

The Garden Classroom is accessible by foot through the entrance on Ardleigh Street, northwest of Washington Lane. Please park on Ardleigh St and walk up the path across from E. Duval Street to the green classroom building.

Directions to the Garden Classroom

*Please note that other directions or GPS to Awbury Arboretum will take you to Cope House, which is NOT walking distance to the Garden Classroom.*

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]]>The post Learning Survival Skills with My Side of the Mountain appeared first on Talking Stick Learning Center.

]]>The first week we sewed bags for foraging supplies. Sam made himself clothes and bags for gathering from deerskin that he tanned. We made ours from fabric, hand sewn, so we could go out and collect acorns and other things on our walks. Early in the fall, we went for a foraging walk around Awbury Arboretum, identifying some of the plants Sam used in the book, sassafras for tea, cattails for flour. I showed them how to identify poison ivy, and also jewelweed, which can be rubbed on skin that has been exposed to poison ivy and stinging nettles. And most important of all, we collected acorns to make the pancakes. This became an obsession with our group, each week they would say “when can we make acorn pancakes like the ones Sam ate in the book?”.

Then began the very long process of prepping the acorns to make flour to make the pancakes. First, the acorns had to be cracked open. They did it with hammers and mallets and rocks. All those acorns we had collected didn’t look like as much when we just had the nut meat. Various days through the fall they worked on cracking open the nuts, just that was a lot of work. I did some research and read that if you boil and rinse the acorns several times, it takes some of the tannin out and makes them less bitter. I did this at home, we just don’t have enough time during our days to do all this prep. We had talked about the tannin and the flavor of the acorns, and that the consistency of Sam’s pancakes would be more like a tortilla than the fluffy pancakes we are used to. None of this lessened their enthusiasm about making pancakes. Also, I told them I would bring some modern pancake batter and we would have both. Finally, in November, it was pancake day. First, we had to grind the nut meat into flour. We did it between rocks like Sam did in the book. The pictures show the tiny bits of acorn dust they were getting from grinding, and then the two little pancakes we made. No worries, no one liked them anyway and we had plenty of present day pancakes to eat.

Three different weeks during the fall we worked on lighting a fire with a flint and steel. One survival skill I learned was that having the right tinder is very important. In my trial run before doing it with the young people, I just lucked into finding great tinder, so I assumed if we just picked some dry grass at Awbury it would work. But when we collected tinder at Talking Stick, everyone struggled the first time to get it to keep burning, the dried grass we found just didn’t light as easily. But even with the struggle, it was fun figuring out how to get a spark, then a little flame. The second and third time I brought dryer lint for them to use as tinder, definitely cheating, Sam didn’t have lint out in the woods. But with the lint we all succeeded lighting fires, by the third time out everyone could light a small fire.

One thing that really helped Sam survive was that he caught a young peregrine falcon, named her Frightful, trained her and taught her to catch meat for him. In class, we talked about raptors and watched videos of them in flight and hunting. I planned a field trip to go to Militia Hill to their Hawk Watch to see hawks migrating and learn about raptors from their volunteers. Unknown to me, one of their volunteers is a licensed falconer and has a pet peregrine falcon that he would bring for us all to see. That field trip was a great day, we had beautiful weather. It was the very end of the migration season, so we didn’t see a lot of raptors, but the volunteers told us a lot and answered our questions. Getting to see Cleo the falcon up close was so exciting.

Tom told us all about her, her story, what is involved in training and taking care of a falcon.

My Side of the Mountain has always been a favorite book of mine, I read it several times when I was young and then again to our children. It was great to take it to another level, to actually learning some of the survival skills that Sam used with the young people at Talking Stick. It certainly made an impression on me, the amount of work that goes into each thing he did, making his own clothes from deer hide, making acorn pancakes, lighting fires, training a falcon. I loved their enthusiasm for both the book and the projects, each week they would come running in saying, ”what are we doing today?”.

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]]>The post Platonic Solids: The First Three Weeks appeared first on Talking Stick Learning Center.

]]>(April 5 -19, 2018) In the past, I’ve often made the mistake of getting out “manipulatives”* to help students discover a certain mathematical concept only to find that the students wanted to engage in open-ended exploration. They weren’t interested in my agenda. So, for this course, I put the Polydrons on the table with no guidelines for two weeks. The students just played with them as we worked on other mathematical questions.

Finally, in week three, I said “This week we are only getting out the Polydrons that are regular polygons. Can you sort them so we can put away the irregular Polydrons?” The students quickly learned what regular polygons are. Then I said, “Let’s make some Platonic solids!” What are they, the students wondered. “There are only two rules: they are constructed from regular polygons and all vertices are the same.” The students spent some time asking questions and understanding these rules, playing with the Polydrons with this goal in mind. “Now we can get to the question,” I announced.

“We haven’t even gotten to the question yet?!” exclaimed the students.

“Yep! The question is this: how many different Platonic solids are there?” After some time, the students had discovered three of them (actually four, but they don’t know yet that they discovered a fourth).

THE HANDSHAKE PROBLEM

Since the students in this course ranged far in age (10-14) and didn’t all know each other, in week 1 I gave a classic math problem that easily generates interaction among students:

“If everyone in a room shakes hands with everyone else, how many handshakes will there be?”

The students reasoned that we have 8 people, so it’s 8 times 8. Wait a minute, do we shake our own hand? No. So we each shake 7 hands, 8 times 7=56. So 56 shakes. Done. Confident they had solved it after 3 minutes. “Are you sure?”

“We have to be sure! Let’s try it out!” declared F. They realized soon that shakes were being double counted. 56 divided by 2=28. So 28 shakes. Done, confident they had solved it after 3 more minutes. I insisted they finish gathering evidence (by completing their experiment). They did get 28 after coming up with way to keep track. Confident they had solved it. (F and Z asked clarifying questions – i.e. what if you do two-handed handshakes? etc)

The following week I asked them to generalize their process, which they did. They even they came up with an algebraic formula for it (with a bit of help from me). “How can you be sure that because this works for 8 people, it would work for all numbers of people?” This introduced doubt big time. That’s great news as far as I’m concerned. I am coaching them to doubt conclusions arrived at through induction. I want to move into proof so that they know beyond a doubt that their formula will work for any number of people. In the spirit of true mathematicians, they're asking does is work for multi-digit numbers of people, etc etc etc.

I also challenged the students to explain how this problem relates to the Platonic Solids. No conjectures yet.

FOILED BY MY EXPECTATIONS AGAIN

The handshake problem did turn out to be a great icebreaker. Actually, the students came up with an icebreaker: Go around the table, say your name, one thing you like to do, and name your favorite Youtuber. (Turns out that two of the students “knew” each other from playing Minecraft online, and loved meeting in person.) “Funny you should mention your favorite Youtuber,” I said, since mine is Vi Hart and I brought in one of her videos to show you today. I showed them one of my favorites: Binary Trees.

My mind was aglow with how the students were going to watch this video, become enraptured by the Sierpinski triangles, and demand time to doodle these on their own. Ha! That didn’t happen at all. I was operating under the false assumption that because something happened once before (7 years ago in a math circle) that it would happen again. No one was interested. Even when I told them that you can make a 3D Sierpinski triangle (a Platonic solid!) out of recycled business cards. “Sounds like a lot of work,” several of them muttered. Foiled by my expectations again. Will I ever learn? OTOH many years ago I tried the Platonic solids with Polydrons activity in a course and those students had no interest in that. These kids now are very interested. It’s actually quite wonderful that the same activities turn out differently each time when you let them.

THE BEAUTY/GLORY OF FUNCTION MACHINES

On the first day, S (an experienced math circle participant) asked, “Are we going to do function machines in this course?” I hadn’t planned on it but decided to throw it into the mix as a crowd pleaser. The math that has come out of this so far has been unexpected and delightful.

For those of you unfamiliar with function machines, you play by saying a number that goes in to the machine and the person operating the machine tells you what comes out. Your job is to guess the rule from a series of ordered pairs (in and out numbers).

When J presented a machine, her rule brought up a discussion of **negative numbers** once it became apparent that when the opposite (negative) of a number went in, the same number came out as it did from the original. So what kind of function would generate the same output from its negative? Turns out that squaring a number does this. What is squaring? What happens when you multiply two negatives? And many more questions… The math behind this that I didn’t mention (and wish I had) is that her function, (x^2 + 50)/2 is an **even function**. In mathematical symbols,

f(x) = -f(x).

I do allow the presenting student to use a calculator. This saves time, keeps everyone interested, and opens up its own Pandora’s Box. When S presented a machine, the out numbers didn’t seem to make sense to him. Everyone waited patiently as he input the numbers into different calculators and got different results. (One of the many things I love about this group is their patience.) I mentioned that not all calculators follow the order of operations. This led to a discussion about what the **order of operations** is. Z broke the ice for this discussion with her comment “The order of operations can be confusing.” We also talked a bit about the necessity of knowing how to use parentheses on calculators.

“How would you get the in number for these two functions from the out number? I asked. This led to a discussion about **inverse functions**. I gave two analogies students are often taught for these – (1) undressing and (2) peeling corn. The students seemed to find the undressing analogy (you take of your shoes before you take off your socks even though you put them on in the opposite order) more accessible. F pointed out a flaw in the corn analogy, that there are obvious things smaller and underneath the kernels with corn.

This exploration of function machines looks likes it’s going to converge with the Platonic solids, as both can be looked at through the lens of symmetry. More on that next time.

Also, next time, I’ll tell you more about some of the other things we’ve been talking about – some logic questions, a paper-folding problem, and more.

Rodi

*Manipulatives are physical objects used as teaching tools. In mathematics, they offer concrete experiences with abstract concepts.

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]]>The post Invariants appeared first on Talking Stick Learning Center.

]]>** Piagetian Conservation Tasks** – We did every activity in this article: http://www.cog.brown.edu/courses/cg63/conservation.html. Conservation tasks basically are about invariants. Some cognitive psychologists posit that the ability to do these tasks is not coachable, while others believe it is. Our group had some variety in who could recognize the invariance. All could spot it sometimes. Most had at least one case of not being able to spot it. Interestingly, whether someone had success at these tasks had no bearing on their examination of the Euler Characteristic.

- Line up cubes and count them. If you change the order or the distance between them does it change the count?
- Redistribute blocks into sets – how does that affect the sum? (Note – the students loved using these wood cubes so much that I had to set up before class second time just to give students a chance to play with them
- Pour water in differently-shaped containers. Is there more in a taller thinner container than in a shorter wider one?
- Flatten a play-doh ball. Does this affect how much play doh is there?
- Weigh a play-doh ball in different shapes – does changing the shape affect the weight?

** 1-2-3 Fingers** – kind of like mathematical Rock Paper Scissors – I say “123” and both you and I hold out however many fingers we want.

- Multiply them – if odd, you win, if even, I win (I win every time – tee hee hee!)
- We did this for three weeks, and by the final week most but not all students had figured out the strategy. Lots of fun! (Thanks to Maria Droujkova for this activity.)
- Play this at home!

**Collaboration through NIM**

- We played the game NIM, which you can learn about here: https://mathforlove.com/lesson/1-2-nim/. We played several versions of the game.
- I told the students that the goal of this game is collaboration, since real-world mathematicians get help from each other in solving problems
- What is the best way to collaborate if we play a game that’s me against the team of all of you?
- Students played this for 5 weeks, with their collaboration and mathematical strategies evolving over the weeks. While the game was fun and the thinking got deeper and more sophisticated over the weeks, the collaboration that I demanded was stressful. I didn’t tell them how. Each of them had different ideas. Some people cared more that their ideas (for collaboration methods and for NIM game strategies) got tried. Others cared more that conflict be avoided. I talked about the challenges and benefits of collaboration a lot!

__Cup game__

- You get 7 cups: 5 upside down a 2 rightside up. Your goal is to get them all rightside up by flipping 2 at a time. (Thanks to Maria again.)
- We had very deep math conversations about this game, getting into parity, testing of many cases, changing the rules to see what would happen, and what would proof require if you want to make generalizations.

__Cross-country race__

- We played the game that is “Example #4” on this handout from the Waterloo Math Circles: http://www.cemc.uwaterloo.ca/events/mathcircles/2010-11/Winter/Senior_Mar23.pdf
- Students changed the names of the cities from unfamiliar Canadian locations to things they made up. This made the game more accessible.
- We played it several times, but not enough to be able to make generalizations. The students who did play it most want to play more to discover what happens when you try other starting points, etc. I promised these pictures so that kids can play at home.

__Strings on Cans__

I brought in a bunch of cans of many sizes. I had multiple strings cut to the length of the diameter of each can.

- How many strings does it take to wrap around the can with no overlap or gaps?
- Turns out everyone found that it takes a little more than 3 strings to wrap around the can, no matter what can they used.
- Is that an invariant? The students thought no. I asked how many tire-diameter-length strings it would take to wrap around the circumference of a tire, and everything thought a lot more than three, despite our hands-on results here. Piagetian cognitive psychologists posit that there is a fixed developmental stage at which students can transfer mathematical patterns to other examples. (Of course, not everyone agrees, and I think that with the discovery of brain plasticity and the modern research on mindset, more people are seeing things like transference as something coachable.) I promise you that I am not using your children as my mini-cognitive-psychology lab!
- A parent in the background asked “Are you talking about pi?” It turns out that yes, we were! That number a little more than three, that ratio of circumference to diameter, is pi (my favorite invariant!)

__Euler History__

- I read a little bit about Leonhard Euler in some of the classes so that the students knew that there was a person being the main problem we were exploring.
- I read from Historical Connections in Mathematics – a series that I love.

__Function Machines__

- One goal was to introduce how to play function machines to students who never did. They are super fun. Ask your children how to play and do it at home! (We used rules like x+1, x+20, 100x+1, x-2, but didn’t discuss them in algebraic terms as I am here.)
- Another goal was to do function machines with invariants and have the students figure out what was invariant, so wanted to use rules like subtracting itself (x-x) or 1 if odd and 0 if even. Ran out of time, though.

Thanks to all of you for sharing your wonderful children in the extra-fun course!

Rodi

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]]>The post The Euler Characteristic for Eight-Year-Olds appeared first on Talking Stick Learning Center.

]]>**BEFORE THE COURSE: THINKING ABOUT IT**

I didn’t want to spoon feed the math in worksheet form where I tip my hat to what’s cool about the Euler Characteristic. I spent a long time developing an approach that I hoped would allow students to make some deductions but not be led too much. (See references at the end for my inspirations.) My big question was how much was enough leading but not too much?

**WEEK 1: PRESENTING THE PROBLEM**

The goal was for students to know what the question is. I spent so much time sent on setting up a dramatic narrative because this is a hard problem for 8-year-olds. It’s especially hard because I was hoping that they would come up with the idea that there is a pattern. I did not want to end up telling them that there’s a pattern.

Here’s the setup:

*I need people to play some roles – a farmer, a horse, a carpenter, a secretary, and an accountant. The farmer wants to build pastures for her horse so that there’s a different crop in each for the horse to graze on. Horse, what do you want to eat? Farmer, can you draw some dots to show where you want the fenceposts to be? Carpenter, can you connect the dots with lines to indicate the fences? The rules are that the fences can’t cross and every post has to be connected to every possible other post. Horse, can you count the pastures? (Fun debate here about whether outside the fences counts as a pasture/region.) Secretary, can you keep track on the board everything that we are counting? Farmer, how many dots did you draw? Carpenter, how many fences did you install? Accountant, what do you get when you add the number of dots to the number of regions? *

*The carpenter’s bid depends up on the numbers of dots, lines, and regions. The farmer will hire the carpenter to do the work if the sum of dots and regions is equal to the number of lines. The farmer and horse really want this thing built so the horse can eat that pizza! Will this thing get built?*

Not everyone understood the math. They did get the general gist that the mathematical requirements were not met to get the fence built. “Let’s change it up!” They tried, but the counting got really tedious and confusing.

**WEEK 2 - UNDERSTANDING THE PROBLEM CONCEPTUALLY**

Since I didn’t think the students really understood the problem last week (as mathematicians often don’t at first), we delved into some background. I asked the students how electricians, tile-installers, painters, and carpenters decide how much to charge for a job (“bidding”). What happens if the bid is too high? Too low? How much would you charge to paint the room we’re sitting in right now? The purpose of this discussion was to demonstrate the ideas of formulas/algorithms/rules for bidding on jobs, since our carpenter is putting in a bid to build the fence.

Also, since the diagram the students constructed was pretty complex, I handed out paper and asked them each to draw their own sample pasture, with “any number of dots.” I hoped that if each student had their own example that they created themselves, that they’d understand the problem better. I also hoped that each would create a less-complex example and therefore would have a better shot at coming up with an answer.

Turns out most of the students had a hard time drawing it and sticking to the rules (no lines crossing, connect everywhere possible). Kids did 19, 20, 25 – covered their pages with dots. I thought to myself that I should repeat this in week 3 with an assistant helping the kids draw. I also thought to myself that I could make a handout with our diagram from the whiteboard and dashed lines so that the students could change it. (Alas, I never did either of these things – the assistant or the handout.)

So no progress on the problem this week. (Just like what happens to mathematicians!)

**WEEK 3 – STARTING TO LOOK FOR PATTERNS**

At this point I started to worry about time. I was starting to get nervous won’t have time to connect it to course topic invariants. Unlike Andrew Wiles, we didn’t have a lifetime to make progress on the problem. Only 3 more sessions after today. So I led more than I had originally wanted to. Used the strategy of starting small and gradually building. Kids wanted to jump ahead to larger numbers but I reigned them in a bit. I neglected to tell them that we were using the strategy of starting small – a lost teachable moment. Oh well, can’t get them all, I had to remind myself later when I was beating myself up mentally a bit about this.

**Week 4 – ASKING QUESTIONS**

I wasn’t sure whether all kids are following the record keeping on the board; we needed to make it more clear. I insisted to trying to do this investigation systematically – increasing by 1 the number of points in each trial - but they still wanted to skip 6. Even when they noticed the gap, they didn’t suggest to try 6. I insisted only because we had only 2 sessions left. (Had we more time, I would’ve just let them skip 6.)

C asked *what if you position the dots a different way?*

S asked *why are all the results odd except when there are 7 dots? *

A asked *why are they always going up by 2 except… *

Someone asked *can we do curved lines?*

Someone else asked *can we ever get a different result?*

The students were excited, curious, asking many questions about the problem. Moreover, they were no longer talking about it in context of farmer/carpenter problem. They were saying “dots/lines/regions” not “posts/fences/pastures.” These 8-year-olds had transcended the material world to the abstract! (After class, I asked myself, “Why are we still calling points dots?!” I set an intention to shift terminology to the more accurate term points, which are different from dots. I never explained that difference but did make the shift.)

**WEEK 5 - DOES THE PATTERN HOLD FOR ALL CASES?**

I brought out the students’ original diagram from week 1, the one with 13 points. The students knew exactly how to assess it now. I asked for a conjecture ahead of time: Do you think you’ll end up with points + regions exceeding the number of lines by 2? Most did. Then they counted and discovered that they still got the same result. So is this an invariant? The consensus was… maybe. Most students said we’d need to try more cases, and C argued vigorously for the need to try different arrangements of dots for the completed trials. One student said we’d need to have a proof. (Most students didn’t know what proof meant, so we didn’t get into because of time. Had we more time, we certainly would have.) So some students worked on trying examples with larger numbers of points while C attacked rearranging the points for several cases (4 points, 5 points, and 6 points).

With about 15 minutes left, we shifted gears to a new problem, “Cross-Country Race,” which I’ll explain in a different report - click here for that one.

**WEEK 6 – STUDENT OWNERSHIP**

I had another activity for today that we all started with (in honor of the approaching Pi Day). During the Pi Day activity, students were anxious about returning to our prior problems. Of the only four students in attendance that day, two were desperate (yes, desperate, I mean it!) to get back to what we were calling at that point “The Horse and Carpenter Problem.” The other two were tired of that problem and really wanted to explore the new problem that we started last week. We didn’t have time for both. It seemed that no matter what we chose, half the class would be disappointed.

“You don’t need me for either of those problems. You own them now. How about you two tackle one and you other two tackle the other?”

They looked at me in seeming shock. “We can’t do them without you!” someone exclaimed.

“Yes, you can. You own these problems!” I handed out markers and that was that. They really didn’t need me. I answered a question here and there, checked their progress when they wanted to show me, and that ended our course.

I promised to publish these pictures so that the students can continue to work on the problems at home. Like real mathematicians often find (and we discussed), six sessions just isn’t enough time to tackle really interesting mathematical problems.

**REFERENCES/INSPIRATION**

Joel David Hamkins. Math for Eight-year-olds: Graph Theory for Kids http://jdh.hamkins.org/math-for-eight-year-olds/

Harvey Mudd College Math Department. Mudd Math Fun Facts: Euler Characteristic https://www.math.hmc.edu/funfacts/ffiles/10001.4-7.shtml

Simon Singh. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem (book)

Owlcation. Some Practical Applications of Mathematics in Everyday Life https://owlcation.com/stem/Some-Practical-Applications-of-Mathematics-in-Our-Everyday-Life

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]]>The post New Topics: The Harlem Renaissance, Trip Planning, and Card Games appeared first on Talking Stick Learning Center.

]]>**The Harlem Renaissance, Part I**

February 15th - March 22

Thursdays, 9-11 am, ages 10-13

5 weeks, $82

This class will focus on the African American musicians, writers, artists,

and leaders from Harlem, NYC in the 1920's. Through the study of the icons

from that time, and through our own artistic expression, we'll draw

sociological and artistic connections between the Harlem Renaissance and

modern day culture. The class may culminate in a day trip to Harlem, NYC

in the spring. Part II will continue on April 5th, after spring break, based on interest.

**International Trip Planning**

February 15th - March 22

Thursdays, 1-3 pm, ages 10-13

5 weeks, $82

Participants will learn how to research a low-budget, culturally-immersive,

international adventure. Choosing a country of interest to them, young

people will plan a mock world travel experience using a variety of online

resources, travel-hacking tips, and guide books. We will discuss

social-conscious tourism and global literacy. Taught by a seasoned

worldschooling mom and teacher who has ventured through several continents

with her kids on the cheap.

**Group Learning through Card Games **

February 15th - March 22

Thursdays, 1-3 pm, ages 10-13

5 weeks, $82

Each week we will learn a new group card game that can be played with just a deck of cards and a few people. We will play this game and also study 1-2 card tricks that are based on mathematical concepts and do not require special decks of cards.

To Register email angie@talkingsticklearningcenter.org

Participants can choose to stay for both classes plus two hours of lunch, social and study time from 11-1. The rate for the full day 9am-3pm is $250 for five weeks.

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]]>The post Reading Shakespeare for Homeschooled Teens appeared first on Talking Stick Learning Center.

]]>We have extended the homeschool Shakespeare class all the way to the week after spring break. If at that time the participants want to keep going, we will choose three more plays to do in April and May (and that will be Shakespeare II).

**Shakespeare I**

6 weeks, 2/22 to 4/5

Thursdays, 1pm to 3pm, $95

Macbeth (2/22, 3/1, 3/8)

A Comedy (students choice) (3/15, 3/22, 4/5 )

This will be a group reading and study of 2 more of Shakespeare's plays: “Macbeth”, and a comedy that the group will select. The first week of each play will be a brief intro to the history and background of the story, a review of some basics on how to read Shakespeare, and handing out of books. We will be using the latest edition of the Folgers Shakespeare Library for each play; it will be helpful for everyone to use the same book and edition so Talking Stick will be supplying the books. At the beginning of each scene, we will assign roles (on a rotating basis) and we will read the play aloud as a group. Everyone reads, and everyone helps and supports each other. The facilitator will pause as needed to review key points and topics. We will read 2 to 3 acts each week. Participants are encouraged to read ahead at home so they are more comfortable with the material. No experience necessary! This is a very casual and fun session; you can usually find us sitting on the floor, in a circle, in one of the beautiful parlor rooms at the Cope House, laughing and supporting each other as together we discover the magic of The Bard.

Costumes are welcome.

To register email angie@talkingsticklearningcenter.org

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]]>The post Embodied Mathematics appeared first on Talking Stick Learning Center.

]]>Here’s a list/description of every activity we did.

** **

**Role-playing the need for math**

In week 1, we acted out scenarios where no numbers were allowed. The students got around this with drawing pictures.

Week 2: no numbers, no pictures

Week 3: no numbers, no pictures, no names of shapes

Week 4: no numbers, no pictures, no names of shapes, no comparison words, and no approximations (at this point we had to use the whiteboard to keep track of all the restrictions)

Week 5: all of the above allowed.

Here were the scenarios:

- Invite me to a party
- Pay me for restoring your sheep’s health
- Resolve a dispute about which army won a battle
- Explain how to cook something (pancakes, cookies, whatever the children knew how to make)
- Explain how to draw a snowman
- Explain how to build a snowman
- Explain how to plant a garden
- Give me directions to your home or your relatives’ home

We had so much fun as students debated and even voted on which words were allowed (Point? Line? Few? Side? Shape? Herd? etc). The students decided each week how the difficulty would be ramped up the following week. They were excited that it would get harder and harder, and it was their idea to make the final week as easy as possible. I didn’t expect this activity to be as popular as it was. The students could have spent the entire 5 weeks doing nothing but this. No one ever got tired of it; they just asked for more and more.

**Simon Says**

We played the game Simon Says but with one twist: with each command, regardless of whether the Simon character said “Simon says,” you have to command the opposite. So if Simon commands “reach your arms to the sky,” the next command has to be “do the opposite of reaching your arms to the sky.” (It’s up to Simon whether to say Simon says, adding in another layer of complexity.) Over the weeks, the students discovered that

- not every command has an opposite
- some commands seem to have multiple opposites (so what does that mean? Does it mean they have no opposite?)
- some commands actually are two commands embedded into one (i.e. stand on your left foot)

If you replace the word opposite with “negate” or “inverse” and replace the word command with “function” the mathematical reasoning involved here may be more apparent. We didn’t use these terms in class, though.

Over the weeks, the game evolved to include the creation of equivalent, not just opposite, expressions. Students could choose to give an opposite or equivalent command and the others had to guess which it was.

**Mirror**

The students stand in a line and the leader strikes a pose. The rest of the group has to mirror it, leading to lots of experimentation with various types of symmetry.

**Ants Go Marching**

The Ants Go Marching is a children’s song that is sung to the tune of “When Johnny Comes Marching Home.” We sang it. “How can we think about or show this idea with our bodies?” I asked, quoting Malke Rosenfeld from the sample chapter of her book Math on the Move. The students first made their bodies into the shapes of the numbers and then wanted to act it out. Problems arose when we didn’t have the right number of people for everyone to stand in the correct formation. In other words, we were playing with divisibility.

**Rhythm Name Patterns**

We clapped the rhythm of every participant’s full name. “How is this mathematical?” I asked, as I asked for every activity during the course. Cyclical patterns, the group came up with after a discussion.

**Sidewalk chalk addition**

I drew a number line from 0 through 8 on the sidewalk. The students jumped to represent operations such as starting on 0 and adding 3, starting on 3 and adding 2, starting on 5 and taking away 4, etc. We did scenarios where the instructions landed them off the line below zero (negative). Then I asked the students to make their bodies face the opposite direction. What happens if you add 2 but you’re facing the other way? What if you take away 3?

In this activity, the wide age spread of the students became apparent. The students ranged from young 5s to a few close to 8. The older students were interested but the younger students wandered away. My original plan for this course had been to do no activities with numbers, but some of the older students begged me to work with numbers right from the start. This activity was to be my compromise. We revisited it a few times for just a few minutes when students needed a break from other activities, but it didn’t become one of our core activities.

**Poi**

I asked my helper Joanna to demonstrate the performance art of poi. “What words would you use to describe what she’s doing?” “How is what she’s doing mathematical?” I was hoping that this would facilitate student’s ability to communicate about math by naming, classifying, and describing poi patterns, and that students would notice the symmetry and periodicity in the motions. They did. Then they wanted to try it. I wasn’t prepared for this, so we couldn’t. (You can do poi with tennis balls in long socks – maybe try it at home.) I was inspired by poi artist Ben Drexler’s article “A Mathematical Approach to Classifying Poi Patterns, Introduction and Basics.”

**Math In Your Feet**

We did an activity from Malke Rosenfeld’s book Math on the Move. (On the book site, click on “Download a Sample” and then find the section “Try it yourself, part 1.”) We invited parents and siblings to do this one too. Students stood in sidewalk-chalk squares and experimented with how many ways they could do certain moves.

**Play Doh Nim**

Play the game Nim with little balls of play doh. In this version, you can smash 1 or 2 on your turn. If you smash the last one you win. This game was another place where the age spread made things difficult so we didn’t return to it on another session, but I plan to do it lots more with other groups. All of the credit for this activity goes to Lucy Ravitch, who described it when she guest-blogged on the Let’s Play Math site.

**Pattern Function Machines**

During the course, one student who had been in math circles before begged to do the activity function machines. (In function machines, students suggest an “in” number, the facilitator reports the “out” number, and the students have to discern the rule after a few examples of ordered pairs.) It took me weeks to figure out how to do this in an embodied way.

We asked the students to stand in a line. The first child was given a red block, the second a blue one, the third a red one. “What color will the next person get?” We did this repeatedly with increasing complexity of patterns and the students creating the patterns. Then we switched and gave the students puppets to hold (and operate, of course). This was tougher since puppets have many more attributes than do wooden cube blocks. The students struggled happily to discern patterns in the line of puppets. The following week we did it with blocks on the table instead of the students carrying them. Had we more time, we would have taken away all props and just had the students stand in certain positions and identify patterns. The eventual mathematical goal would be to move toward abstraction by eventually moving into words then symbols/numbers, but that was not the goal of this course.

Many thanks to helpers Joanna (for facilitating many of the activities) and Maria (for being an extra set of hands). Also to you parents for sharing your wonderful children with us!

Rodi

*Here’s our course description: Neuroscience has provided empirical evidence of what we intuitively knew all along: that counting on your fingers enhances learning. The discipline of embodied mathematics employs gesturing and physical interactions with the environment to develop conceptual understanding and to facilitate articulation of mathematical concepts. Year after year, young students come into Math Circle with the idea that mathematics is all about quick computation and nothing else. This course will open students’ minds to the reality that math is about more than numbers and can be explored with more than a computational approach. We’ll use our bodies and surroundings to examine symmetry, 2D and solid geometry, equivalence, measurement, spatial reasoning, and arithmetic computation.

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]]>This class runs for about eight weeks and entails reading a variety of ethnographies, which are extensive studies of particular cultures. We examine instances of cultural relativism, ethnocentrism, quantitative research, racism, identity politics, and more throughout the history of the academic discipline of anthropology. For example, we compare and contrast early ethnographic work with current trends in anthropology. We look at and discuss customs that may be very different from our own as well as analyzing aspects of our own culture(s). We explore concepts such as gender, childhood and religion as well as customs such as ancestor worship, mourning rituals, puberty initiation, and anthropomorphism. The format consists of power point presentations, discussions, activities and exercises. A highlight is developing ideas about our own utopian visions by using what we have learned about other cultures.

*8 weeks, 9am - 11am, $125*

In this course, participants will explore poetic elements, themes, strategies, and issues as are relevant to the poems being studied, including the historical/cultural contexts in which they were written. Readings include works from diverse cultural contexts, including, for example, poems by women, African Americans, other minorities, and non-Western writers. We will engage in close and imaginative readings with the goal of appreciating each poem’s unique contribution to the art, as well as developing our ability to articulate our relationship with the piece. Participants will have the option to generate new work through exercises and experiments inspired by the piece we are exploring.

*15 weeks, 1pm - 2pm, $125*

In this introduction to the discipline of Karate, students will analyze and demonstrate the application of traditional karate techniques, including blocking, punching, kicking, striking, and stances, as well as an understanding of traditional martial arts etiquette, and respect for themselves, others, and the art. Study of the martial arts develops a measurable sense of accomplishment and an integration of mind and body, contributing to greater self-esteem as well as improving flexibility, strength, and general physical health.

*15 weeks, 2pm - 3pm, $125*

For more information or to register for teen classes email angie@talkingsticklearningcenter.org

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